“…In recent years, piezoelectric actuators (PEAs) have attracted much attention due to their advantages, such as a large output force, compact size, high resolution, and quick response. They have a wide range of potential applications in the fields of micro-manipulation [ 1 ], micromechanical manufacturing [ 2 ], super-precision processing [ 3 ], adaptive optical compensation [ 4 , 5 , 6 ], and robotics [ 7 , 8 , 9 , 10 ]. However, piezoelectric ceramic materials have hysteretic nonlinear characteristics of multi-valued mapping and frequency dependence [ 11 ].…”